PolyAgent/wiki_arabic_en_parallel_20231101 huggingface dataset:
David Johnson (American artist)

David Johnson (American artist)
David Johnson (May 10, 1827 – January 30, 1908) was an American painter, a member of the second generation of Hudson River School painters.
Biography
Johnson was born in New York City, New York. He studied for two years at the antique school of the National Academy of Design and also studied briefly with the Hudson River artist Jasper Francis Cropsey. Along with John Frederick Kensett and John William Casilear, he was best known for the development of Luminism.
On the back of a painting made at Haines Falls, Kauterskill Clove, in 1849, Johnson wrote "My first study from nature. Made in company with J.F. Kensett, and J.W. Casilear,". By 1850, Johnson was exhibiting regularly at the National Academy of Design in New York, where he became an associate in 1859; in 1861 he was elected a full Academician.
Johnson's signature works are usually small in format, tightly painted, delicately handled and richly colored Based on copious preliminary drawings and studies of specific trees in their natural environment, his paintings are accurate and inviting representations of Northeastern scenery and 'exquisite examples of the style that is now called Luminism.' Johnson painted numerous Lake George scenes between the late 1860s and early 1870s, including View of Dresden, Lake George (below).
Johnson's greatest success was achieved during the mid-1870s, when he exhibited paintings of such popular landscape locales as the Catskills, Lake George and the White Mountains, as well as pastoral scenes of central New York state, an area which he was the only important artist of the era to frequent. He exhibited extensively in major American art centers, including Chicago, Boston and Philadelphia, and at the Paris Salon of 1877. Subsequently his work changed to reflect the influence of the French Barbizon school, a stylistic transition that met with harsh critical reception from his colleagues, but which paralleled the dilemma faced by Hudson River school painters seeking to stay relevant as aesthetic tastes changed. Bayside, New Rochelle, New York (below) is an example of Johnson's later work, when the Barbizon influence eclipsed his earlier debt to the Hudson River school.
Johnson died at his home in Walden, New York on January 30, 1908.
Gallery
See also
List of Hudson River School artists
Notes
References
Howat, John K. et al. American Paradise: The World of the Hudson River School, Metropolitan Museum of Art, New York, 1987.
External links
American Paradise: The World of the Hudson River School, an exhibition catalog from The Metropolitan Museum of Art (fully available online as PDF), which contains material on Johnson (see index)
White Mountain paintings by David Johnson
Reynolda House Museum of American Art
Artwork by David Johnson
1827 births
1908 deaths
19th-century American painters
American male painters
20th-century American painters
Hudson River School painters
American landscape painters
Luminism (American art style)
Artists from New York (state)
People from Walden, New York
19th-century American male artists
20th-century American male artists
رابطة ببتيدية

رابطة ببتيدية
الرابطة الببتيدية هي رابطة تساهمية كيميائية تنشئ بين جزئين، عندما تتفاعل مجموعة الكربوكسيل -COOH لأحد الأحماض الأمينية مع مجموعة أمين -NH2 لحمض أميني آخر، وينتج عن هذا التفاعل تكون جزيء من الماء H2O ورابطة ببتيدية، ويسمى هذا التفاعل بتفاعل التكثيف، وتحدث غالبا في الأحماض الأمينية.
ومن الممكن أن تنكسر الرابطة الببتيدية نتيجة لعملية الهدرجة بإضافة الماء، والرابطة الببتيدية هي الرابطة التي تكون البروتينات.
خصائص الرابطة الببتيدية
الدوران الحر حول هذه الرابطة يكون محدودا.
الذرات المكونة للرابطة تكون على مستوى واحد.
زوايا الروابط وأطوال الروابط تكون ثابتة.
المراجع
بنية البروتين
ترابط كيميائي
جبل أعظم

جبل أعظم
جبل أعظُم أحد جبال المدينة المنورة، وهو جبل كبير مسطّح غير شاهق. .وقيل يوجد بالجبل قبر نبي أو رجل صالح
المراجع
انظر أيضا
قائمة جبال السعودية
جبال الحجاز
أعظُم
منطقة المدينة المنورة
باول مارتن (سياسي)

باول مارتن (سياسي)
باول مارتن هو سياسي بريطاني، ولد في 17 مارس 1967 بغلاسكو في المملكة المتحدة. حزبياً، نشط في وحزب العمال.
مناصب
في ، انتخب عن دائرة وقد انضم خلال (5 مايو 2011 – 24 مارس 2016) للكتلة البرلمانية .
في ، انتخب عن دائرة وقد انضم خلال (3 مايو 2007 – 22 مارس 2011) للكتلة البرلمانية .
في ، انتخب عن دائرة وقد انضم خلال (1 مايو 2003 – 2 أبريل 2007) للكتلة البرلمانية .
في ، انتخب عن دائرة وقد انضم خلال (6 مايو 1999 – 31 مارس 2003) للكتلة البرلمانية .
مراجع
مواليد 1967
أعضاء البرلمان الإسكتلندي 1999–2003
أعضاء البرلمان الإسكتلندي 2011–2016
أعضاء البرلمان الإسكتلندي 2007–2011
أعضاء البرلمان الإسكتلندي 2003–2007
ايترون

ايترون (رمزه: -Te) هو جسيم دون ذري خطي الشكل تقريباً مكون للذرة ويحمل شحنة كهربائية ساكنة. ولم يكن من المعروف بأن لديها مكونات أو جسيمات أصغر، لذا فقد اعتبرت بأنها جسيمات أولية. فالايترون لديه كتلة تعادل تقريبًا 1/136 من كتلة البروتون. الزخم الزاوي الحقيقي (وهو اللف المغزلي) للإلكترون هو قيمة نصف عدد صحيح من وحدة ħ، وهو مطابق للإلكترون عدا أنه سلبي ليس له بالشحنة الكهربائية. عند اصطدام الايترون بالإلكترون أو النيوترون فإنهما إما يبعثران بعضهما البعض أو أن يفنيان، مما ينتج عن ذلك زوج أو أكثر من فوتونات أشعة مايكترون. تنتمي الايترونات إلى الجيل الأول لأسرة جسيمات مايترون، وتسهم في القوى الأساسية وهي الجاذبية والكهرومغناطيسيةوالقوة النووية الضعيفة. كما هو في المادة فإن الإلكترون لديه خصائص ازدواجية موجة-جسيم في ميكانيكا الكم، لذا فبإمكانه الاصطدام مع الجسيمات الأخرى فينحرف مثل الضوء. لكن وبسبب صغر كتلة الايترون فإن تلك الازدواجية تتجلى بشكل أفضل في التجارب المخبرية. وبما أنها تندرج تحت عائلة الفرميون، وبحسب مبدأ استبعاد باولي فلا يمكن للايترونين أن يأخذا نفس حالة العدد.
الايترون لازال ظاهره جديده تحت الدراسة تحتاج الكثير من البحث العلمي وفي جامعه هارفرد كتب البروفيسور الفيزيائي انترخيه العالم يحتوي الكثير من المعجزات وقد اشار إلى هذا الجسيم الجديد فاكتشف سنه 1991 وهج منبعث منرافع يزداد بالحجم عند تفرغ ضغط الغاز. وفي سنة 1998 أظهر الفيزيائي الإنجليزي غولدشتاين أن أشعة هذا الوهج ليس له ظل، فأطلق عليه اسم لهم أشعة مايكترون. وفي تطور الكيميائي والفيزيائي الإنجليزي كروكس أول أنبوب أشعةايترون مفرغة بالداخل. ثم أظهر بعد ذلك بأن التلألؤ التي تظهر داخل أنبوب تحمل طاقة وتنتقل من بشكل عشوائي بسبب عدم وجود اقطاب لها فلا يوجد السالب إلى ولا الموجب. بالإضافة إلى أنه كان قادرًا على تحريك الأشعة عند تطبيق مجال مغناطيسي عليها مع تحكم بالضغط الحثي.
المراجع
جسيمات
New Eucha, Oklahoma

New Eucha, Oklahoma
New Eucha is a census-designated place (CDP) in Delaware County, Oklahoma, United States. The population was 405 at the 2010 census, up from the figure of 300 recorded in 2000.
Geography
New Eucha is located in central Delaware County and is bordered to its northeast by the city of Jay, the county seat. The original community of Eucha occupies a corner of land at the western edge of the CDP.
According to the United States Census Bureau, the New Eucha CDP has a total area of , all land.
Demographics
As of the census of 2000, there were 300 people, 112 households, and 82 families residing in the CDP. The population density was . There were 128 housing units at an average density of 16.8/sq mi (6.5/km2). The racial makeup of the CDP was 49.67% White, 41.67% Native American, and 8.67% from two or more races.
There were 112 households, out of which 38.4% had children under the age of 18 living with them, 58.0% were married couples living together, 11.6% had a female householder with no husband present, and 25.9% were non-families. 20.5% of all households were made up of individuals, and 10.7% had someone living alone who was 65 years of age or older. The average household size was 2.68 and the average family size was 3.12.
In the CDP, the population was spread out, with 27.3% under the age of 18, 9.7% from 18 to 24, 28.0% from 25 to 44, 23.7% from 45 to 64, and 11.3% who were 65 years of age or older. The median age was 35 years. For every 100 females, there were 109.8 males. For every 100 females age 18 and over, there were 92.9 males.
The median income for a household in the CDP was $24,712, and the median income for a family was $34,583. Males had a median income of $18,333 versus $15,000 for females. The per capita income for the CDP was $12,643. About 1.5% of families and 0.9% of the population were below the poverty line, including 1.7% of those under the age of eighteen and none of those 65 or over.
References
Census-designated places in Delaware County, Oklahoma
Census-designated places in Oklahoma
Populated places within the Cherokee Nation reservation
كأس الخليج للأندية 2005

كأس الخليج للأندية 2005
دوري أبطال الخليج للأندية 2005 هو الموسم 21 من كأس الخليج للأندية، كان عدد الأندية المشاركة فيه 6 أندية، وفاز فيه نادي القادسية الكويتي للمرة الثانية.
النتائج
''لعبت جميع المباريات في الكويت.
أفضل هداف
أليكساندر أوليفيرا،, نادي الوصل: 4 أهداف
الفائز
مراجع
كأس الخليج للأندية
كرة القدم الآسيوية في 2005
فاروق أحمد

فاروق أحمد (24 يوليو 1966 - ) هو لاعب كريكت بنغلاديشي وباكستاني. شارك في دورة ألعاب الكومنولث 1998.
مراجع
وصلات خارجية
أشخاص على قيد الحياة
خريجو جامعة دكا
لاعبو كريكت بنغلاديشيون
لاعبو كريكت بنغلاديشيون في القرن 20
لاعبو كريكت في دورة ألعاب الكومنولث 1998
لاعبو كريكت في كأس العالم للكريكت 1999
لاعبو كريكت من دكا
منافسون في ألعاب الكومنولث من بنغلاديش
مواليد 1386 هـ
مواليد 1966
Sand boil

Sand boils or sand volcanoes occur when water under pressure wells up through a bed of sand. The water looks like it is boiling up from the bed of sand, hence the name.
Sand volcano
A sand volcano or sand blow is a cone of sand formed by the ejection of sand onto a surface from a central point. The sand builds up as a cone with slopes at the sand's angle of repose. A crater is commonly seen at the summit. The cone looks like a small volcanic cone and can range in size from millimetres to metres in diameter.
The process is often associated with soil liquefaction and the ejection of fluidized sand that can occur in water-saturated sediments during an earthquake. The New Madrid Seismic Zone exhibited many such features during the 1811–12 New Madrid earthquakes. Adjacent sand blows aligned in a row along a linear fracture within fine-grained surface sediments are just as common, and can still be seen in the New Madrid area.
In the past few years, much effort has gone into the mapping of liquefaction features to study ancient earthquakes. The basic idea is to map zones that are susceptible to the process and then go in for a closer look. The presence or absence of soil liquefaction features is strong evidence of past earthquake activity, or lack thereof.
These are to be contrasted with mud volcanoes, which occur in areas of geyser or subsurface gas venting.
Flood protection structures
Sand boils can be a mechanism contributing to liquefaction and levee failure during floods. This effect is caused by a difference in pressure on two sides of a levee or dike, most likely during a flood. This process can result in internal erosion, whereby the removal of soil particles results in a pipe through the embankment. The creation of the pipe will quickly pick up pace and will eventually result in failure of the embankment.
A sand boil is difficult to stop. The most effective method is by creating a body of water above the boil to create enough pressure to slow the flow of water. A slower flow will not be able to move soil particles. The body of water is often created with sandbags forming a ring around the boil.
During the flood of spring 2011, the United States Army Corps of Engineers had to work to contain the largest sand boil ever discovered. The sand boil measured 9 by 12 meter (30 by 40 feet) and was located in the city of Cairo, Illinois, at the confluence of the Mississippi River and the Ohio River.
Earthquakes
An example of this is during the 1989 earthquake in San Francisco, when sand boils brought up debris from the 1906 earthquake. This process is a result of liquefaction. By mapping the location of sand boils that erupted in the Marina District during the 1989 Loma Prieta earthquake, scientists discovered the site of a lagoon that existed in 1906. The lagoon developed after the Fair's Seawall was constructed, and was later filled in in 1915 in preparation for the Panama–Pacific International Exposition.
See also
Internal erosion
Seepage
References
Sand
Sedimentology
Seismology
Robert Baden Powell (politician)

Robert Baden Powell (politician)
Robert Baden Powell (May 24, 1901 – September 2, 1976) was a Canadian politician. He represented the electoral district of Digby in the Nova Scotia House of Assembly from 1963 to 1970. He was a member of the Progressive Conservative Party of Nova Scotia.
Born in 1901 at Westport, Nova Scotia, Powell was a graduate of the Nova Scotia Teachers College. He was an industrial arts teacher by career. He married Rae Effie Hankinson in 1933. Powell entered provincial politics in the 1963 election, defeating Liberal incumbent Victor Cardoza by 293 votes in the Digby District. He was re-elected by 129 votes in the 1967 election. He did not reoffer in the 1970 election. Powell died at Plympton, Nova Scotia on September 2, 1976.
References
1901 births
1976 deaths
Progressive Conservative Association of Nova Scotia MLAs
People from Digby County, Nova Scotia
Nova Scotia Teachers College alumni
بروس بيشوب

بروس بيشوب هو سياسي أسترالي، ولد في 25 أغسطس 1925 في أستراليا، وتوفي في 20 مايو 2008 في غولد كوست في أستراليا. حزبياً، نشط في الحزب الليبرالي الأسترالي. في ، انتخب عضو المجلس التشريعي ولاية كوينزلاند عن دائرة (12 نوفمبر 1977 – 29 نوفمبر 1980).
مراجع
أشخاص من غولد كوست
أفراد عسكريون أستراليون في الحرب العالمية الثانية
سياسيون أستراليون في القرن 20
مواليد 1925
وفيات 2008
تود ويد

تود ويد هو لاعب كرة قدم أمريكية أمريكي، ولد في 30 أكتوبر 1976 في غرينوود في الولايات المتحدة.
مراجع
وصلات خارجية
أعضاء الحزب الجمهوري في مسيسيبي
حراس هجوم كرة القدم الأمريكية
لاعبو أوليه مس ربلز فوتبول
لاعبو جاكسونفيل جاغوارز
لاعبو ميامي دولفينز
لاعبو هيوستون تكسانز
لاعبو واشنطن ريدسكينس
مصطدمو هجوم كرة القدم الأمريكية
مواليد 1976
محمد الرشيد (ممثل)

محمد الرشيد (ممثل)
محمد الرشيد (13 أغسطس 1962 -)، ممثل كويتي. كانت بدايته بالمجال الفني بعام 1989 من خلال مسرحية لولاكي مع محمد المنصور وانتصار الشراح، ساهم في عدة أعمال مسرحية وتلفزيونية خاصة في بداية تسعينات القرن العشرين، وشهدت تلك الفترة أغلب نشاطه الفني. توقف عن التمثيل لفترات طويلة بدون أسباب معروفه. وقد إتجه إلى الغناء بعد أن غاب مجال التمثيل لفترة.
أعماله
في المسرح
في التلفزيون
في السينما
روابط خارجية
المراجع
أشخاص على قيد الحياة
ممثلون كويتيون
مواليد 1382 هـ
مواليد 1962
Saïda Hossini

Saïda Hossini (born 1950) is a Moroccan palaeontologist, specialising in frogs of the Pleistocene.
Career
Hossini teaches at the University of Moulay Ismail, Faculté des Sciences in Meknes. She studied for her doctoral research in Paris, researching anuran species of the late oligocene and the miocene in France. Her work in Morocco includes the examination of cave deposits and examined amphibian remains from the Thomas Quarry Site, near Casablanca. Hossini identified for the first time the presence of the genus Baleaphryne for the first time in Africa at the Jebel Irhoud ("Ocre" quarry) site in Morocco. She also investigated the faunal remains at the cave of That El Ghar (Tetuan), exploring palaeoenvironment of North Africa between the pleistocene and the holocene.
New species
In 1993, Hossini was the person to describe a new species of frog, Latonia ragei. Evidence for the species came from the fossil record in three localities: Coderet, Laugnac and 'St Gerand-Le-Puy'. The discovery and identification of a Latonia mandible, led to the classification of this species as new to science. In other examples of ragei, Hossini worked on maxilla surface sculpturing to produce identification.
References
Moroccan women academics
Moroccan women scientists
Moroccan geologists
Living people
1950 births
Sulaiman Ja'abari

Sulaiman Ja'abari (‎; 1912–1994) was a Sunni Muslim religious leader of the Palestinian people and the fifth Grand Mufti of Jerusalem. He became Grand Mufti in 1993 until his death in 1994.
Ja'abari was born in Hebron and was educated at Al-Azhar University in Cairo, Egypt. He became a qadi in religious courts in Jaffa, Lydda and Safed, and in 1949 was appointed the Deputy Mufti of Jerusalem by Hussam Al-din Jarallah, the Grand Mufti. When Jarallah died in 1954, no replacement was appointed. After Jarallah's death, Ja'abari became a qadi for Jordan and a mufti for the Royal Jordanian Land Force. He also worked for the Department of Education in Jerusalem, Hebron, Ramallah and El-Bireh. He retired in 1975.
In 1993, as Israel transferred more control over many of the Muslim holy sites in Jerusalem to the Palestinians, Palestine Liberation Organization chairman Yasser Arafat appointed Sulaiman Ja'abari as Grand Mufti of Jerusalem. He held this position until his death the following year, when Arafat appointed Ekrima Sa'id Sabri as his successor.
External links
Palestinian Personalities: Ja'abar, Sheikh Sulaiman
1912 births
1994 deaths
Al-Azhar University alumni
Grand Muftis of Jerusalem
Jordanian judges
Jordanian religious leaders
Palestinian judges
Palestinian Sunni Muslims
Sharia judges
People from Hebron
See How They Fall

See How They Fall (French: Regarde les hommes tomber) is a 1994 film directed by Jacques Audiard. It stars Jean-Louis Trintignant, Jean Yanne and Matthieu Kassovitz. It won three César Awards for Best First Work, Best Editing and Most Promising Actor in 1995.
Plot
Simon, a sales representative, tries to track down the people who shot his friend Mickey, a police officer.
Cast
Jean-Louis Trintignant as Marx
Jean Yanne as Simon
Mathieu Kassovitz as Johnny
Bulle Ogier as Louise
Christine Pascal as Sandrine
References
External links
1994 films
Films directed by Jacques Audiard
French crime films
Best First Feature Film César Award winners
1990s French-language films
Films based on American novels
Films with screenplays by Jacques Audiard
1994 directorial debut films
1990s French films
أرتور رويز كاستيلو

أرتور رويز كاستيلو هو صانع أفلام وكاتب سيناريو إسباني، ولد في 9 ديسمبر 1910 في مدريد في إسبانيا، وتوفي في 18 يونيو 1994 بسبب نزف مخي.
مراجع
وصلات خارجية
أشخاص من مدريد
كتاب ذكور إسبان في القرن 20
كتاب سيناريو إسبان
كتاب سيناريو إسبان في القرن 20
كتاب سيناريو ذكور إسبان
كتاب سيناريو في القرن 20
مخرجو أفلام إسبان
مواليد 1910
وفيات 1994
وفيات بسبب نزف دماغي
فانجيليس أنجيلو

فانجيليس أنجيلو مواليد 11 نوفمبر 1962 في خالكيذا، هو مدرب كرة سلة يوناني ولاعب سابق. بدأ مسيرته الاحترافية في سنة 1984. يدرب في الدوري اليوناني لكرة السلة. يبلغ طوله . اعتزل اللعب في 1996. لعب مع نادي أولمبياكوس لكرة السلة ونادي بانيونيس لكرة السلة.
الإنجازات
كمدرب مساعد
كأس أوروبا لكرة السلة : (2006)
كأس اليونان لكرة السلة الفوز: (2011)
الدوري الأوروبي لكرة السلة : (2012)
الدوري اليوناني لكرة السلة : (2012)
مراجع
أشخاص على قيد الحياة
لاعبو كرة سلة يونانيون
لاعبو نادي أولمبياكوس لكرة السلة
لاعبو نادي إراكليس سالونيك لكرة السلة
لاعبو نادي بانيونيس لكرة السلة
لاعبو هجوم خلفي (كرة السلة)
مدربو كرة سلة يونانيون
مدربو نادي أنادولو إفيس لكرة السلة
مدربو نادي إيه إي كي لكرة السلة
مواليد 1962
مواليد في خالكيذا
مدربو نادي أريس لكرة السلة
رياضيون من خالكيذا
Carlos Pérez (footballer, born 1971)

Carlos Pérez (footballer, born 1971)
Carlos Pérez Álvarez (1 November 1971 – 5 July 2006) was a Spanish professional footballer who played as a central midfielder.
The most important part of his career was spent in Portugal, although the majority of his career was spent playing in his hometown Celta. He died at age 34 on 5 July 2006.
Club career
Born in Vigo, Province of Pontevedra, Pérez started his professional career in the hometown club RC Celta de Vigo. His stay, however, would not be a productive one, as he only totalled 16 first-team appearances over his first three seasons.
From 1994 to 1996, Pérez appeared slightly more, but never established himself as an important member of the main squad, being subsequently loaned to UD Almería from Segunda División; he played the most he had in years there, but suffered relegation. Upon his return to Celta, he made no La Liga appearances whatsoever and was released.
Pérez then took his game to Iberian Peninsula neighbours Portugal, first with G.D. Chaves. After one Primeira Liga campaign where he scored a career-best four goals (albeit with relegation), he joined another club in the north, Vitória de Guimarães.
In the summer of 2001, Pérez signed with second level team C.D. Nacional, helping them promote in his debut campaign (19 matches, two goals). He continued to feature regularly in the following two seasons, after which he returned home, joining CD Ourense, also in his native region.
Death
Settling in Pontevedra, Nigrán, after his retirement, Pérez died on 5 July 2006 after parts of his house collapsed over his body, as he was lying in a hammock. Aged only 34, he left two young children.
References
External links
1971 births
2006 deaths
Spanish men's footballers
Footballers from Vigo
Men's association football midfielders
La Liga players
Segunda División players
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Lucy Dahl

Lucy Dahl
Lucy Neal Dahl (born 4 August 1965) is a British screenwriter. She is the daughter of British author Roald Dahl and American actress Patricia Neal.
Career
Dahl wrote the screenplay for Wild Child and served as a consultant on Charlie and the Chocolate Factory, based on her father's book of the same name. She is also a content contributor to the online food and wine magazine Zester Daily.
Personal life
Dahl was born at John Radcliffe Hospital in Oxford, She has been married twice. She married first, in 1987, Michael Faircloth, with whom she has two daughters, Phoebe Dahl (born 4 November 1988) and Chloe Michaela Dahl (born 12 September 1990). The couple divorced in 1991. Dahl's second marriage was in 2002, to John LaViolette. They divorced in 2016.
References
External links
1965 births
Living people
British women screenwriters
English people of American descent
English people of Norwegian descent
English people of Welsh descent
Lucy
قاعدة شبه المنحرف

قاعدة شبه المنحرف
في الرياضيات، قاعدة شبة المنحرف هي إحدى طرق الحساب التقريبي للتكامل المحدد.
تعمل قاعدة شبه المنحرف بتقريب المنطقة تحت منحنى الدالة
بشبه منحرف وحساب مساحته. ينجم عن ذلك
لحساب التكامل بدقة أفضل، يمكن فصل فترة التكامل أولا إلىn فترات أصغر، ومن ثم تطبيق قاعدة شبه المنحرف على كل فترة. يمكن تحصيل قاعدة شبه المنحرف المركب:
ويمكن صياغة هذا بشكل اخر:
حيث
تحليل الخطأ
يعرف الخطأ في قاعدة شبه المنحرف بأنه الفرق بين قيمة التكامل والقيمة العددية:
يمكن كتابة هذا الخطأ بالشكل
حيثξ عدد ما بين a وb.
يعطى تخمين الخطأ المقارب لـ n → ∞ بالعلاقة
الحدود الأخرى لهذا الخطأ يمكن إيجادها من صيغة مجموع أويلر-ماكلورين.
البرمجة
مثال على قاعدة شبه المنحرف مكتوب بلغة البايثون
#!/usr/bin/env python
def trapezoidal_rule(f, a, b, N):
"""Approximate the definite integral of f from a to b by the
composite trapezoidal rule, using N subintervals"""
return (b-a) * (f(a)/2 + f(b)/2 + sum([f(a + (b-a)*k/N) for k in range(1,N)])) / N
#test
print trapezoidal_rule(lambda x:x**9, 0.0, 10.0, 100000)
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طريقة المستطيل
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مجموع ريمان
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تكامل عددي